Step by Step
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The Rayleigh criterion
A telescope's resolution follows θ = 1.22 λ/D (the Rayleigh criterion), where a larger aperture (D) produces finer resolution.
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How interferometry improves resolution
By combining light coherently from two or more telescopes, the effective resolution becomes λ/baseline (the distance between the telescopes) rather than λ/individual mirror diameter — allowing far finer resolution than any single telescope could achieve alone.
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Radio versus optical interferometry examples
Radio VLBI can use continental-scale baselines, achieving microarcsecond resolution. Optical interferometry (used by facilities like VLTI, CHARA, and NPOI) typically uses baselines of about 200-330 meters, sufficient to resolve stellar surfaces (like Betelgeuse) or measure binary star separations.
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The Event Horizon Telescope and future directions
The EHT uses an Earth-sized baseline to resolve a black hole's shadow. An array of telescopes essentially mimics a single giant mirror — but only for measuring angular sizes, not for imaging faint, extended objects. Future space-based interferometry (avoiding the atmosphere entirely) could enable direct imaging of exoplanets.
Applied Walkthrough
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According to the Rayleigh criterion, a single telescope's resolution depends directly on its aperture size — but rather than building one impossibly enormous mirror, astronomers can instead combine light coherently from multiple separate telescopes.
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This technique — interferometry — effectively achieves resolution based on the DISTANCE between the telescopes (the baseline), rather than any individual telescope's own mirror size, allowing dramatically finer resolution than any single instrument could provide.
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Optical interferometers like the VLTI or CHARA, using baselines of a few hundred meters, can resolve details as fine as the surface features of a nearby giant star like Betelgeuse — while radio VLBI, using continental or even Earth-sized baselines, achieves microarcsecond resolution.
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This exact Earth-spanning approach is what allowed the Event Horizon Telescope to resolve the shadow of a supermassive black hole — though it's worth noting that interferometry excels specifically at measuring angular sizes and fine details, rather than imaging faint, extended objects the way a single large telescope would.
Exam Application
Exams test whether you understand that interferometry's resolution depends on the baseline distance between telescopes (not any single telescope's mirror size), and whether you know specific examples at both radio and optical wavelengths and their approximate scales.
⚠ Common Trap
The most common trap is assuming interferometry works the same way for all observing purposes as a single giant telescope would — interferometry specifically excels at measuring fine angular details (like stellar surfaces or a black hole's shadow), but it isn't equivalent to a single giant mirror for imaging faint, extended objects.
✓ Quick Self-Check
1. What is the Rayleigh criterion, and what does it relate?
θ = 1.22 λ/D — it relates a telescope's resolution to its aperture (D) and observing wavelength (λ).
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2. How does interferometry improve resolution beyond a single telescope's limit?
By combining light from multiple telescopes, achieving resolution based on the baseline distance between them, rather than any single mirror's diameter.
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3. What baseline scale do optical interferometers like VLTI typically use, and what can they resolve?
About 200-330 meters; sufficient to resolve stellar surfaces or binary star separations.
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4. What baseline did the Event Horizon Telescope use, and what did it resolve?
An Earth-sized baseline; it resolved a black hole's shadow.
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5. Is interferometry equally good for imaging faint, extended objects as for measuring angular sizes?
No — it's specifically excellent for angular size measurements, but not equivalent to a single giant mirror for imaging faint, extended objects.
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